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Anomalous topological Floquet states

Pierre Delplace

Since the discovery of the quantum spin Hall effect, the search for novel topological insulating states has been stimulating tremendous efforts, impacting many areas of physics beyond semi-conductors physics. In particular it was proposed, and then observed in photonic lattices, that specific periodic drives can lead to unusual dynamical topological states, referred to as topological Floquet states. Whereas such driving protocols were first proposed to simply dynamically trigger a topological phase transition, it was later realized that novel topological states, with no equilibrium (or static) counterpart, can be induced : the so-called anomalous topological Floquet states. More specifically, the usual topological index used to account for the existence of boundary states, namely the first Chern number, vanishes, and an other "dynamical" invariant must be used.

In this seminar, I will discuss the roles of two different symmetries in this context. First I will show how a Z2-valued dynamical invariant can be defined when the evolution operator is constrained by time-reversal symmetry, thus generalizing the pioneering work by Kane and Mele to periodically driven systems. Then I will discuss the recently introduced "phase rotation symmetry" that was proposed to achieve anomalous states.


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